A new algorithm for generalized fractional programs

A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual†to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual†parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual†approach is less influenced by scaling.fractional programming;generalized fractional programming;Dinkelbach-type algorithms;quasiconvexity;Karush-Kuhn-Tucker conditions;duality

Light-induced hexatic state in a layered quantum material

The tunability of materials properties by light promises a wealth of future applications in energy conversion and information technology. Strongly correlated materials such as transition-metal dichalcogenides (TMDCs) offer optical control of electronic phases, charge ordering and interlayer correlations by photodoping. Here, we find the emergence of a transient hexatic state in a TMDC thin-film during the laser-induced transformation between two charge-density wave (CDW) phases. Introducing tilt-series ultrafast nanobeam electron diffraction, we reconstruct CDW rocking curves at high momentum resolution. An intermittent suppression of three-dimensional structural correlations promotes a loss of in-plane translational order characteristic of a hexatic intermediate. Our results demonstrate the merit of tomographic ultrafast structural probing in tracing coupled order parameters, heralding universal nanoscale access to laser-induced dimensionality control in functional heterostructures and devices

Duality for equilibrium problems under generalized monotonicity

Duality is studied for an abstract equilibrium problem which includes, among others, optimization problems and variational inequality problems. Following different schemes, various duals are proposed and primal-dual relationships are established under certain generalized convexity and generalized monotonicity assumptions. In a primal-dual setting, existence results for a solution are derived for different generalized monotone equilibrium problems within each duality scheme

Reporting of sex as a variable in cardiovascular studies using cultured cells

<p>Abstract</p> <p>Background</p> <p>Chromosomal complement, including that provided by the sex chromosomes, influences expression of proteins and molecular signaling in every cell. However, less than 50% of the scientific studies published in 2009 using experimental animals reported sex as a biological variable. Because every cell has a sex, we conducted a literature review to determine the extent to which sex is reported as a variable in cardiovascular studies on cultured cells.</p> <p>Methods</p> <p>Articles from 10 cardiovascular journals with high impact factors (<it>Circulation</it>, <it>J Am Coll Cardiol</it>, <it>Eur Heart J</it>, <it>Circ Res</it>, <it>Arterioscler Thromb Vasc Biol</it>, <it>Cardiovasc Res</it>, <it>J Mol Cell Cardiol</it>, <it>Am J Physiol Heart Circ Physiol</it>, <it>J Heart Lung Transplant and J Cardiovasc Pharmacol</it>) and published in 2010 were searched using terms 'cultured' and 'cells' in any order to determine if the sex of those cells was reported. Studies using established cell lines were excluded.</p> <p>Results</p> <p>Using two separate search strategies, we found that only 25 of 90 articles (28%) and 20 of 101 articles (19.8%) reported the sex of cells. Of those reporting the sex of cells, most (68.9%; n = 31) used only male cells and none used exclusively female cells. In studies reporting the sex of cells of cardiovascular origin, 40% used vascular smooth-muscle cells, and 30% used stem/progenitor cells. In studies using cells of human origin, 35% did not report the sex of those cells. None of the studies using neonatal cardiac myocytes reported the sex of those cells.</p> <p>Conclusions</p> <p>The complement of sex chromosomes in cells studied in culture has the potential to affect expression of proteins and 'mechanistic' signaling pathways. Therefore, consistent with scientific excellence, editorial policies should require reporting sex of cells used in <it>in vitro </it>experiments.</p

Combined relaxation method for mixed equilibrium problems

We consider a general class of equilibrium problems which involve a single-valued mapping and a nonsmooth bifunction. Such mixed equilibrium problems are solved with a combined relaxation method using an auxiliary iteration of a splitting-type method for constructing a separating hyperplane. We prove the convergence of the method under the assumption that the dual of the mixed equilibrium problem is solvable. Convergence rates are also derived. © 2005 Springer Science+Business Media, Inc

Gauss-Seidel method for multi-valued inclusions with Z mappings

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented. © 2011 Springer Science+Business Media, LLC

Characterizations of relatively generalized monotone maps

New concepts of relative monotonicity were introduced in Konnov (Oper Res Lett 28:21-26, 2001a) which extend the usual ones. These concepts enable us to establish new existence and uniqueness results for variational inequality problems over product sets. This paper presents first-order characterizations of new (generalized) monotonicity concepts. Specialized results are obtained for the affine case. © Springer-Verlag 2007

Performance of chemically modified reduced graphene oxide (CMrGO) in electrodynamic dust shield (EDS) applications

Electrodynamic Dust Shield (EDS) technology is a dust mitigation strategy that is commonly studied for applications such as photovoltaics or thermal radiators where soiling of the surfaces can reduce performance. The goal of the current work was to test the performance of a patterned nanocomposite EDS system produced through spray-coating and melt infiltration of chemically modified reduced graphene oxide (CMrGO) traces with thermoplastic high-density polyethylene (HDPE). The EDS performance was tested for a dusting of lunar regolith simulant under high vacuum conditions (~10-6 Torr) using both 2-phase and 3-phase configurations. Uncapped (bare) devices showed efficient dust removal at moderate voltages (1000 V) for both 2-phase and 3-phase designs, but the performance of the devices degraded after several sequential tests due to erosion of the traces caused by electric discharges. Further tests carried out while illuminating the dust surface with a UV excimer lamp showed that the EDS voltage needed to reach the maximum cleanliness was reduced by almost 50% for the 2-phase devices (500 V minimum for rough and 1000 V for smooth), while the 3-phase devices were unaffected by the application of UV. Capping the CMrGO traces with low-density polyethylene (LDPE) eliminated breakdown of the materials and device degradation, but larger voltages (3000 V) coupled with UV illumination were required to remove the grains from the capped devices.Comment: 22 pages, 7 figure

An FPTAS for optimizing a class of low-rank functions over a polytope

We present a fully polynomial time approximation scheme (FPTAS) for optimizing a very general class of non-linear functions of low rank over a polytope. Our approximation scheme relies on constructing an approximate Pareto-optimal front of the linear functions which constitute the given low-rank function. In contrast to existing results in the literature, our approximation scheme does not require the assumption of quasi-concavity on the objective function. For the special case of quasi-concave function minimization, we give an alternative FPTAS, which always returns a solution which is an extreme point of the polytope. Our technique can also be used to obtain an FPTAS for combinatorial optimization problems with non-linear objective functions, for example when the objective is a product of a fixed number of linear functions. We also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor, unless P = NP. We prove this by showing a similar hardness of approximation result for supermodular function minimization, a result that may be of independent interest